Solution:
The probability of an event is expressed as
[tex]Pr(\text{event)}=\frac{\text{Number of desired outcome}}{Number\text{ of possible outcome}}[/tex]Given a fair cube which has its faces numbered 1 to 6 as [1,2,3,4,5,6].
This implies that the number of possible outcome equals 6.
Given that a 6 will appear when rolled, the probability is thus
[tex]\begin{gathered} Pr(6)=\frac{\text{Number of }6\text{ in the far cube}}{Number\text{ of possible outcome}}\text{ } \\ =\frac{1}{6} \\ \end{gathered}[/tex]When the cube is rolled four times, the probability thus becomes
[tex]\begin{gathered} Pr(^{_{}}6)=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6} \\ \Rightarrow Pr(^{_{}}6\text{ four times)=}\frac{1}{1296} \end{gathered}[/tex]Hence, the probability that the number 6 will appear four times is
[tex]\frac{1}{1296}[/tex]